A Coin Trick

Take a couple of coins -- 5 dollar and 2 dollar (any two similar coins of 
18 mm.  and 25 mm. in diameter will do).
Then, on a sheet of paper, cut out a circle equal to the circumference of the 2 dollar coin.

Do you think the 5-dollar coin will get through this hole?

There is no catch to the problem; it is genuinely geometrical.

Similar Figures

This problem is meant for those who understand geometrical similarity.

Answer the following two questions:

1) Are the two triangles in the picture similar?

2) Are the outer and inner rectangles of the picture frame similar?

The Height of a Tower

There is a very big tower in your town, but you do not know its height. You have, however, a photograph of the tower.

Can it help you to find the real height?

Two Watermelons

A man is selling two watermelons. One is one-quarter bigger than the other, but costs one and a half times more. Which one would you buy?

A Brick

A regular-size brick weighs 4 kilogrammes.
How much will a similar toy brick, four times smaller but made of the same material, weigh?

The Way of the Fly

On the wall inside a cylindrical glass container, three centimeters from the upper circular base,
there is a drop of honey. On the lateral surface, diametrically opposite it, there is a fly.

Show the fly the shortest route to the honey.

The diameter of the cylinder is 10 centimetres and the height 20.

Don’t expect the fly to find this way itself and thus facilitate the solution of the problem: for that it would have to be well versed in geometry, and that is something beyond a fly’s ability.

Find a Plug (3)

And here is yet another problem of the same type.
Find a plug for the three apertures in the picture

*** click here for answer ***